Put a rack in the upper third of the oven and preheat the oven to 350°F. Lightly butter a 9-inch baking dish.
For the topping, in a medium bowl, combine the flour, sugar, and salt. Add the butter and, using your fingers, work the butter into the flour mixture. Quickly break down the butter until some of the pieces are the size of oat flakes and some are the size of peas. Add the oats and pecans and toss together.
For the filling, in the prepared baking dish, toss together the strawberries, fresh ginger, sugar, ground ginger, and cornstarch. Toss well. Add a handful of the topping mixture to the fruit mixture and toss lightly. Sprinkle the remaining topping mixture over the top.
Bake until the fruit juices are bubbling and the top is golden brown, 40 to 45 minutes. Remove the baking dish from the oven and let cool for about 30 minutes before serving.
